Chop 1/2 cup fresh basil and 1 clove garlic. Cut tough ends off 1 pound of asparagus and thinly slice on the bias. Halve 1 pint cherry or grape tomatoes.
Whisk the olive oil, basil, 3 tablespoons lemon juice, shallot, garlic, 1/2 teaspoon salt, and 1/2 teaspoon pepper together in a bowl large enough to hold the pasta salad.
Cook the asparagus in 4 quarts boiling water seasoned with 1 tablespoon salt until tender, about 3 minutes. Transfer the asparagus to a colander using a slotted spoon (do not discard the boiling water) and run under cold water until cool. Shake out any excess water and toss with the vinaigrette.
Return the water to a boil, add 2 (9 ounce) packages of tortellini, and cook until tender, following the package instructions. Drain the tortellini thoroughly, then toss while hot with the asparagus and dressing. Refrigerate until chilled, about 30 minutes.
Toast the pine nuts in a small skillet over medium heat until golden and fragrant, about 5 minutes. Just before serving, stir the toasted pine nuts, tomatoes, and Parmesan into the salad and season with salt and pepper.
Serve with apple slices and any remaining tomatoes.